ON THE CAUCHY-RASSIAS STABILITY OF A CLASS OF TRANSLATED ADDITIVE FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

Abstract

In this paper, we give the general solution of the functional equation and we investigate the Cauchy-Rassias stability of this equation in a Banach space. The concept of Cauchy-Rassias stability was originated in the paper of Th. M. Rassias, On the stability of the linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300 in which the Hyers-Ulam-Rassias stability of the linear mapping was proved subject to an unbounded Cauchy difference.